{"id":"https://openalex.org/W1994999396","doi":"https://doi.org/10.2307/2271946","title":"Relativized realizability in intuitionistic arithmetic of all finite types","display_name":"Relativized realizability in intuitionistic arithmetic of all finite types","publication_year":1978,"publication_date":"1978-03-01","ids":{"openalex":"https://openalex.org/W1994999396","doi":"https://doi.org/10.2307/2271946","mag":"1994999396"},"language":"en","primary_location":{"id":"doi:10.2307/2271946","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271946","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002700076","display_name":"Nicolas D. Goodman","orcid":null},"institutions":[{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Nicolas D. Goodman","raw_affiliation_strings":["Suny at Buffalo, Amherst, NY 14226"],"affiliations":[{"raw_affiliation_string":"Suny at Buffalo, Amherst, NY 14226","institution_ids":["https://openalex.org/I63190737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002700076"],"corresponding_institution_ids":["https://openalex.org/I63190737"],"apc_list":null,"apc_paid":null,"fwci":2.7217,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.90469341,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"43","issue":"1","first_page":"23","last_page":"44"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/realizability","display_name":"Realizability","score":0.8754817843437195},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.736339271068573},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.6667904853820801},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5130235552787781},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.46265488862991333},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.4379673898220062},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4261331558227539},{"id":"https://openalex.org/keywords/kripke-semantics","display_name":"Kripke semantics","score":0.41283297538757324},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3834133446216583},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37725159525871277},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.18405723571777344},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1454870104789734},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.1374691128730774},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10850971937179565},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.09937039017677307}],"concepts":[{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.8754817843437195},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.736339271068573},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.6667904853820801},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5130235552787781},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.46265488862991333},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.4379673898220062},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4261331558227539},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.41283297538757324},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3834133446216583},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37725159525871277},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.18405723571777344},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1454870104789734},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.1374691128730774},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10850971937179565},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.09937039017677307},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2271946","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271946","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183740104","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183740104","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W60489380","https://openalex.org/W120666666","https://openalex.org/W1483568252","https://openalex.org/W1566235828","https://openalex.org/W1699512023","https://openalex.org/W1854750410","https://openalex.org/W2001469185","https://openalex.org/W2043566933","https://openalex.org/W2069764971"],"related_works":["https://openalex.org/W4390724922","https://openalex.org/W1969083063","https://openalex.org/W2403418519","https://openalex.org/W4253721198","https://openalex.org/W4205932853","https://openalex.org/W206382595","https://openalex.org/W3128849256","https://openalex.org/W3175327018","https://openalex.org/W3024382762","https://openalex.org/W2154784560"],"abstract_inverted_index":{"In":[0,63,93],"this":[1,153,165,241],"paper":[2],"we":[3,53,65,73,95,116,175],"introduce":[4],"a":[5,46,67,97,106,118,130,150,173,232],"new":[6,79,131],"notion":[7,18,58,103,124],"of":[8,25,33,39,45,59,86,100,108,121,133,152,187,196,210,220,235,240],"realizability":[9,32,60,123],"for":[10,111],"intuitionistic":[11,87,189,214],"arithmetic":[12,88,190],"in":[13,51,61,71,83,89,114,139,146,158,193],"all":[14,90,226],"finite":[15,91,211],"types.":[16,92,227],"The":[17],"seems":[19],"to":[20,22,77,128,248],"us":[21],"capture":[23],"some":[24,43,84],"the":[26,30,37,134,177,194,202],"intuition":[27],"underlying":[28],"both":[29],"recursive":[31],"Kjeene":[34],"[5]":[35],"and":[36,48,55,70,104,125,141,144,218,222],"semantics":[38],"Kripke":[40],"[7].":[41],"After":[42],"preliminaries":[44],"syntactic":[47],"recursion-theoretic":[49],"character":[50],"\u00a71,":[52],"motivate":[54],"define":[56],"our":[57,101,122,147],"\u00a72.":[62],"\u00a73":[64],"prove":[66,105],"soundness":[68],"theorem,":[69],"\u00a74":[72],"apply":[74],"that":[75],"theorem":[76,110,137,242],"obtain":[78,176],"information":[80],"about":[81],"provability":[82],"extensions":[85],"\u00a75":[94],"consider":[96,117],"special":[98],"case":[99],"general":[102],"kind":[107],"reflection":[109],"it.":[112],"Finally,":[113],"\u00a76,":[115],"formalized":[119,192],"version":[120],"use":[126],"it":[127],"give":[129],"proof":[132],"conservative":[135,233],"extension":[136,186,234],"discussed":[138],"Goodman":[140],"Myhill":[142],"[4]":[143],"proved":[145,157],"[3].":[148],"(Apparently,":[149],"form":[151],"result":[154],"is":[155,231,243],"also":[156],"Mine":[159],"[13].":[160],"We":[161],"have":[162],"not":[163],"seen":[164],"paper,":[166],"but":[167],"are":[168],"relying":[169],"on":[170],"[12].)":[171],"As":[172],"corollary,":[174],"following":[178],"somewhat":[179],"strengthened":[180],"result:":[181],"Let":[182,198],"\u03a3":[183,199,206,229,247],"be":[184,201,249],"any":[185],"first-order":[188,251],"(HA)":[191],"language":[195],"HA.":[197],"\u03c9":[200,230],"theory":[203],"obtained":[204,244],"from":[205],"by":[207,245],"adding":[208],"functionals":[209],"type":[212],"with":[213],"logic,":[215],"intensional":[216],"identity,":[217],"axioms":[219],"choice":[221,224],"dependent":[223],"at":[225],"Then":[228],"\u03a3.":[236],"An":[237],"interesting":[238],"example":[239],"taking":[246],"classical":[250],"arithmetic.":[252]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}